A a name is crossed out, but it readable. Should the name be entered into the batch or skipped?
If it is not replaced and you can read it, you should index it.
You will find the following guidance in the General Indexing Guidelines (3rd) section of your Project Instructions. I have bolded the pertinent instruction.
Crossed-Out, Corrected, Canceled, or Void Information
When information was crossed out, corrected, canceled, or marked void, follow the instructions for “crossed out” that match the situation.
You're welcome, Bob.